Cracking the code of place value: The relationship between place and value takes years to master.

Place value, which underlies the meanings of multidigits, encompasses the principle of position and base-10 rules. To understand 65, one needs to know that the digits 6 and 5 occupy different positions and thus represent ordered values of different magnitudes (i.e., the principle of position) and that the value of each position is determined by base-10 rules (i.e., the rightmost position is 100, followed by 101, 102, etc.). Without the principle of position, children cannot construct meanings for multidigits. Previous studies have shown that children do not know the exact value of digit positions until the early elementary school years, but less is known about the acquisition of positional knowledge for multidigits. To study when and how children construct a relationship between position and value, we explore when children begin to know that the leftmost digit represents the largest value and whether such knowledge relates to learning number names. Children ages 4 to 7 years, from primarily Caucasian, middle-class families were asked to compare different pairs of multidigits. Some comparisons (e.g., 12 vs. 21) required knowledge of positional property, and some did not (e.g., 35 vs. 36). We found that as a group, 6-year-old children could recruit positional knowledge to compare multidigits. We also found that children who knew the number names of both multidigits in a comparison pair were above chance on multidigit comparison. Our results shed light on the developmental steps toward acquiring place-value notation and highlight a role of learning number names for learning positional property of the place-value notation. (PsycInfo Database Record (c) 2021 APA, all rights reserved).